Vol. 35, No. 2, 1970

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On p-spaces and wΔ-spaces

Dennis K. Burke

Vol. 35 (1970), No. 2, 285–296

In this paper the relationships between p-spaces and wΔspaces are investigated. It is shown that strict p-spaces, p-spaces, and wΔ-spaces are all equivalent in the class of completely regular 𝜃-refinable spaces. There is an example of a completely regular, countably compact space (and thus a wΔ-space) which is not a p-space. An example is given of a T2 locally compact space (and thus a p-space) which is not a wΔ-space. In the last section we give some conditions for p-spaces or wΔ-spaces to be developable.

Mathematical Subject Classification
Primary: 54.20
Received: 29 January 1970
Published: 1 November 1970
Dennis K. Burke